Sunday, March 26, 2017
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Seminar - 'eXtended Hybridizable Discontinuous Galerkin (X-HDG)', by Sònia Fernández

Wednesday, March 29th, 2017. Time: 12h

Place: O.C. Zienkiewicz Conference Room, C1 Building, UPC Campus Nord, Barcelona.


The eXtended Hybridizable Discontinuous Galerkin method (X-HDG) is an efficient HDG method [1], incorporating the eXtended Finite Element (X-FEM) philosophy for the solution of problems with material interfaces or voids. X-HDG was first proposed for heat problems with voids in [2] and has been further developed in for the solution of bimaterial heat and flow problems. X-HDG inherits the advantages of X-FEM methods [3] (a level-set representation of the interface is considered, and the computational mesh is not required to fit the interface, simplifying and reducing the cost of mesh generation and, in particular, avoiding continuous remeshing for evolving interfaces or boundaries), while keeping the computational efficiency, stability, accuracy, optimal convergence and superconvergence of HDG.

    • [1]    B. Cockburn, J. Gopalakrishnan, R. Lazarov. “Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems”, SIAM JNA 2009.
    • [2]    Gürkan, C.; Sala-Lardies, E.; Kronbichler, M.; Fernández-Méndez, S., “eXtended Hybridizable Discontinous Galerkin (X-HDG) for void problems”, Journal of Scientific Computing 2016.
    • [3]    T.P. Fries, T. Belytschko, “The extended/generalized finite element method: An overview of the method and its applications”, IJNME 2010.

Sònia Fernández, from LÀCAN (Numerical Methods in Applied Sciences and Engineering) -Department of Civil and Environmental Engineering.